$\left\{ \frac{6}{7} + \frac{7\frac{3}{4} - 6\frac{1}{2}}{\frac{7}{3} imes 9} ight\}$ of Rs. 42 is equal to :

Question

$\left\{ \frac{6}{7} + \frac{7\frac{3}{4} - 6\frac{1}{2}}{\frac{7}{3} 	imes 9} ight\}$ of Rs. 42 is equal to :

Accepted Answer

To solve the given problem and verify why Option 3 is the correct answer, we need to evaluate the expression step by step.

The expression given is:

$$
\left\{ \frac{6}{7} + \frac{7\frac{3}{4} - 6\frac{1}{2}}{\frac{7}{3} \times 9} \right\} \text{ of Rs. 42}
$$

Let's break it down:

1. **Simplify the expression inside the brackets:**

- First, convert the mixed numbers to improper fractions:
     - $7\frac{3}{4} = \frac{31}{4}$
     - $6\frac{1}{2} = \frac{13}{2}$

- Subtract the fractions:
     $$
     \frac{31}{4} - \frac{13}{2} = \frac{31}{4} - \frac{26}{4} = \frac{5}{4}
     $$

- Calculate $\frac{7}{3} \times 9$:
     $$
     \frac{7}{3} \times 9 = \frac{63}{3} = 21
     $$

- Divide the result of the subtraction by the product:
     $$
     \frac{5}{4} \div 21 = \frac{5}{4} \times \frac{1}{21} = \frac{5}{84}
     $$

2. **Add the result to $\frac{6}{7}$:**

- Find a common denominator and add:
     $$
     \frac{6}{7} + \frac{5}{84} = \frac{72}{84} + \frac{5}{84} = \frac{77}{84}
     $$

3. **Calculate the final value:**

- Multiply the result by Rs. 42:
     $$
     \frac{77}{84} \times 42 = \frac{77 \times 42}{84} = \frac{3234}{84} = 38.5
     $$

Thus, the expression evaluates to Rs. 38.50, confirming that Option 3 is indeed the correct answer.

**Explanation for Incorrect Options:**

- **Option 1 (Rs. 77):** This option is incorrect because the calculation of the expression does not yield Rs. 77. The multiplication and division steps clearly show that the result is Rs. 38.50.

- **Option 2 (Rs. 38):** This option is incorrect because the precise calculation results in Rs. 38.50, not Rs. 38. The difference arises from the fractional part that must be accounted for.

- **Option 4 (Rs. 39.50):** This option is incorrect because the calculated value of the expression is Rs. 38.50. The additional amount in this option does not match the result of the arithmetic operations performed.

In conclusion, the detailed step-by-step calculation supports Option 3 as the correct answer, which is Rs. 38.50.